Heat transfer from laminar flow through cylindrical tubes

Zusammenfassung Die Differentialgleichung für Wärmeleitung in einer durch ein zylindrisches Rohr strömenden Flüssigkeit, die wie bekannt schon öfters behandelt wurde, wird in der vorliegenden Arbeit mittels der konfluenten hypergeometrischen Funktion gelöst. Bei der Berechnung des ersten Eigenwertes wird von den neulich herausgegebenen Tafeln Gebrauch gemacht.     

Heat transfer to magnetohydrodynamic flow in a flat duct

Zusammenfassung Die Untersuchung befasst sich mit der Wärmeübertragung von den Wänden eines flachwandigen Kanals auf eine elektrisch leitende Flüssigkeit bei erzwungener Laminarströmung und in Gegenwart eines quergerichteten Magnetfeldes. Betrachtet wird der Fall konstanter Wandtemperatur mit variierender innerer Wärmeentwicklung durch viskose und elektrische Energiedissipation. Die massgebende Differentialgleichung wird durch eine Differenzengleichung ersetzt und mit der elektronischen Rechenmaschine gelöst. Als Resultat wird die Nusseltzahl angegeben, für die Prandtlzahl 1, die Hartmannzahlen 0, 4, 10 und die Graetzzahlen von 10 bis 10 000, wobei die Kennzahlen für Zähigkeit und elektrische Feldstärke als Parameter auftreten.     

Heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate

This paper concentrates on the heat transfer analysis of the steady flow of an Oldroyd 8-constant fluid due to a suddenly moved plate. The heat transfer analysis has been carried out for the prescribed surface temperature. Employing homotopy analysis method, the developed system of equations are solved analytically. The convergence of the obtained series solution is established. The influence of pertinent parameters on temperature profiles and Nusselt number is shown and discussed through several graphs. Further, a comparison between temperature profiles of Newtonian and Oldroyd fluids is also made.     

On rotational viscous flow through a tube

Zusammenfassung Für die Eigenwerte und Eigenfunktionen eines Eigenwertproblems, auf dasL. Collatz undH. Görtler im Zusammenhang mit einer kürzlichen Untersuchung [3] über Rohrströmung mit schwachem Drall geführt worden sind, werden asymptotische Näherungsformeln angegeben, die insbesondere die höhern Eigenwerte mit grösserer Genauigkeit als in [3] zu berechnen gestatten. Auch zur Ermittlung der niedrigen Eigenwerte wird ein einfaches Verfahren vorgeschlagen. Die Ergebnisse werden numerisch mit denen von [3] verglichen.

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This paper was prepared under a National Bureau of Standards contract with American University and was supported by the Office of Naval Research.     

Heat transfer for laminar flow through parallel porous disks of different permeability

The problem of temperature distribution and heat transfer for laminar flow through two parallel porous disks of different permeability, has been investigated when the flow is entirely due to injection and/or suction at the two disks. Viscous dissipation terms have been included in the energy equation and the injection and/or suction velocities at the two disks are assumed to be small. The boundaries are kept at constant temperatures. The variation of temperature and Nusselt numbers at the two disks has been graphically depicted for various values of the injection and suction velocities.     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

Large Eddy Simulation of a flow through circular tube bundle

The Large Eddy Simulation approach is used to perform a numerical simulation of a flow around a circular tube bundle. The model uses the immersed boundaries technique to represent tube geometry in the Cartesian grid. Simulation is conducted in an area away from the boundaries, where the flow is considered homogenous and, thus, the three Cartesian directions are considered periodic. The results are compared with experimental data in terms of mean velocity and turbulence quantities, showing good agreement in general.     

Effect of slip on the linear stability of flow through a tube

A theoretical investigation of the linear stability of the flow of a Newtonian fluid through a tube is presented using an alternative boundary condition to the standard no-slip condition. The linear stability analysis is based on the classical method of infinitesimal axially symmetric harmonic perturbations super-imposed on the steady state solution. In this analysis the standard no-slip boundary condition is replaced with the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter, which may be regarded as a positive slip length. The aim of this analysis is to assess the effect of a nonzero slip length on the behavior of infinitesimal disturbances in the flow through a tube. It is demonstrated that for positive slip the rate of decay of the least damped disturbance is reduced, although the flow still remains stable to all infinitesimal disturbances of the type considered, as it does for the no-slip boundary condition.     

Effect of slip on the linear stability of flow through a tube

A theoretical investigation of the linear stability of the flow of a Newtonian fluid through a tube is presented using an alternative boundary condition to the standard no-slip condition. The linear stability analysis is based on the classical method of infinitesimal axially symmetric harmonic perturbations super-imposed on the steady state solution. In this analysis the standard no-slip boundary condition is replaced with the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter, which may be regarded as a positive slip length. The aim of this analysis is to assess the effect of a nonzero slip length on the behavior of infinitesimal disturbances in the flow through a tube. It is demonstrated that for positive slip the rate of decay of the least damped disturbance is reduced, although the flow still remains stable to all infinitesimal disturbances of the type considered, as it does for the no-slip boundary condition.     

Heat transfer for flow past permeable bed

A theoretical analysis of the temperature distribution is presented for a viscous liquid through a two dimensional parallel channel formed by an impermeable upper plate and permeable lower plate under the action of a constant pressure gradient past a porous bed. It is shown that the flow properties are dependent on the parametersα, β andσ characteristic of the permeable material. The effects of these parameters on temperature distribution and Nusselt number at both the plates are studied in detail.     

Heat transfer from a porous sphere in low Reynolds number flow

This paper deals with the problem of the effect of permeability in the steady state heat transfer from a single porous sphere at low Reynolds number with the assumptionsPr=0(1) andR<1. The solution is sought by the method of matched asymptotic expansions. The Nusselt number,Nu, for isothermal sphere has been calculated for different values ofk, wherek being the permeability associated with the porosity of the sphere. We notice that the Nusselt number increases as the permeability increases in the range 0<R<0.35 with the Prandtl numberPr=0.7, the rate of increase is very small, while for the Reynolds numberR0.35 Nusselt number decreases ask increases and the rate of decrease is large.

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Zusammenfassung In dieser Arbeit wird der Einfluss der Durchlässigkeit von einer porösen Kugel auf den Wärmeübergang behandelt, bei kleiner Reynolds-ZahlR undPr=0(1). Die Lösung wird mit der Methode der angepassten asymptotischen Entwicklung gewonnen. Die Nusselt'sche ZahlNu für die isotherme Kugel wurde für verschiedene Werte des Durchlässigkeits-Koeffizientenk ausgerechnet. Man findet, dass die Nusselt'sche Zahl (schwach) zunimmt mit der Durchlässigkeit für 0<R<0.35 mitPr=0.7, wogegen fürR0.35Nu (stark) abnimmt mit wachsendemk.

     

Uniform suction/blowing effect on flow and heat transfer due to a stretching cylinder

The present paper presents a numerical solution of flow and heat transfer outside a stretching permeable cylinder. The governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved numerically using the Keller-box method. The main purpose of the present study is to investigate the effects of the governing parameters, namely the suction/injection parameter, Prandtl number, and Reynolds number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. The results are shown graphically. The values of the skin friction coefficient and the Nusselt number are presented in tables.     

Heat transfer in a peristaltic flow of MHD fluid with partial slip

In the present note, we have discussed the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. The governing equations of motion and energy are simplified using a long wave length approximation. A closed form solution of the momentum equation is obtained by Adomian decomposition method and an exact solution of the energy equation is presented in the presence of viscous dissipation term. The expression for pressure rise is calculated using numerical integration. The trapping phenomena is also discussed. The graphical results are presented to interpret various physical parameter of interest. It is found that the temperature field decreases with the increase in slip parameter L, and magnetic field M, while with the increase in P_r and E_c, the temperature field increases.     

Heat transfer and Reynolds' analogy in a turbulent flow with heat release

Zusammenfassung Es wird die Wärmeübertragung von und zu einer voll entwickelten, wärmeabgebenden, turbulenten Strömung in einem Rohr analysiert. Durch die Anwendung der Laplace-Transformation wird die partielle Randwertaufgabe der Temperaturverteilung in einem Rohr von kreisförmigem Querschnitt auf eine gewöhnliche Sturm-Liouvillesche Randwertaufgabe zurückgeführt. Die entsprechenden Eigenwerte und Eigenfunktionen können nun mittels des Ritzschen Verfahrens für verschiedene Werte der Prandtlschen und Reynoldsschen Zahlen berechnet werden.Die Verteilung der Temperatur und des Wärmeflusses entlang der Wand erhält man in Form einer Reihe, deren Glieder diese Eigenwerte und Eigenfunktionen enthalten. Durch Verallgemeinerung des Prandtlschen Wärmequellen-Satzes wird die Reynoldssche Analogie der Wärmeübertragung und der flüssigen Reibung für eine wärmeabgebende turbulente Strömung erweitert.Die genaue asymptotische Wärmefluss und Temperaturverteilung, die man erhält, gestattet eine Abschätzung des Fehlers, den man bei einer Anwendung der Ritzschen Methode und der daraus folgenden Reihenentwicklung erhalten würde. Diese Analyse kann für die wärmeabgebenden turbulenten Strömungen in Atomreaktoren angewendet werden.

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The results presented in this paper were obtained in the course of research sponsored by the Office of Scientific Research of the ARDC, US Air Force under Contract AF 18 (603)-104.